Budgeted Quotient-Residual Guidance for Frozen Pocket-Conditioned Molecular Diffusion

2026-09-25

AI Summary

This study addresses the challenge that frozen molecular diffusion models struggle to directly optimize quotient-space objectives, such as distance and contact constraints, while retraining remains prohibitively expensive. To overcome this, we propose a budgeted quotient-residual guidance method that balances geometric orientation with sampling motion scale through level-set elevation and a trust-budget mechanism, thereby activating quotient-space constraints during inference without retraining. By integrating KL-divergence and kinetic-energy interpretations, equivariant conditioning, and a budget allocation algorithm, our approach achieves lightweight model correction. Evaluated on TargetDiff, the proposed method significantly improves ligand generation validity while preserving diversity, all without modifying the backbone network. This work establishes an efficient, training-free paradigm for controlled molecular generation.

Abstract

Pocket-conditioned molecular diffusion updates ambient atom coordinates, but many lead-optimization objectives are expressed on quotient features such as distances, contacts, and anchored substructures. We introduce budgeted quotient-residual guidance (QRG), an inference-time correction that makes these quotient objectives active without retraining the molecular generator. QRG lifts quotient covectors to metric-horizontal ambient directions and delivers them through a trust budget set by the frozen sampler's own step norm: quotient geometry chooses the direction, while sampler motion bounds the scale. We derive the horizontal lift, closed-form sampler-budget update, KL/kinetic interpretation around a frozen reverse step, equivariance conditions, and a product-budget split for budget-capped section and residual controls. Controlled quotient tasks confirm that sampler-relative delivery activates signals that raw local quotient gradients leave dormant. On frozen TargetDiff backbones, official seed-0 CBGBench ligand-generation/editing sweeps show practical quality-runtime gains: Local-QRG improves validity from 0.815 to 0.864 on fragment growing, 0.664 to 0.707 on scaffold hopping, and 0.681 to 0.712 on linker design, while PredNext-QRG improves fragment/scaffold and remains near-neutral on linker. Novelty remains 1.000 and diversity is preserved in the matched multi-seed molecular slice, giving task-dependent improvements without sampler retraining or backbone modification. Overall, QRG provides a lightweight route to quotient-aware inference for frozen molecular samplers with explicit runtime accounting.

Problem

• molecular diffusion
• lead optimization
• quotient features
• frozen sampler
• molecule generation

Innovation

• Quotient-Residual Guidance
• Molecular Diffusion
• Frozen Sampler
• Horizontal Lift
• Lead Optimization